Ann. For. Sci. 66 (2009) 108 Available online at:c© INRA, EDP Sciences, 2009 www.afs-journal.orgDOI: 10.1051/forest/2008080

Original article

Potential productivity of forested areas based on a biophysical model.A case study of a mountainous region in northern Spain

Raquel Benavides1*, Sonia Roig2, Koldo Osoro1

1 SERIDA, Área de Sistemas de Producción Animal, Apdo 13, 33300 Villaviciosa, Asturias, Spain2 Centro de Investigación Forestal (CIFOR)-INIA, 28040, Madrid, Spain

(Received 5 May 2008; accepted 5 October 2008)

Keywords:geostatistics /GIS /land use planning /modelling /yields

Abstract• Today’s forest managers face a number of important challenges involving an increasing need forprecise estimates of forest structure and biomass, potential productivity or forest growth. The objec-tive is to develop a model for potential productivity in a mountainous region of Spain. The model com-bines climatic, topographic and lithological data using a variant of a traditional biophysical model:the Paterson index.• In a first approach, the climatic productivity is assessed by modelling the required parameters usingdifferent geostatistical techniques and software supported by GIS. A second approach includes thecorrection of the former productivity classes considering the different lithological facies. The poten-tial forest productivity model involves the integration of both models.• Finally, data from the National Forest Inventory (NFI) are used to compare the real and potentialyield data within different regions of the studied area.• The results of these analyses demonstrate the usefulness of the model, particularly in mountainousregions, where no significant differences are found between the data from the NFI and the model, butthey also show the discrepancies between the estimates and real data when the latter are consideredfor different tree species, diameter classes or management.

Mots-clés :techniques géostatistiques /SIG /gestion de l’usage des sols /modélisation /rendements

Résumé – Productivité potentielle des forêts à partir d’un modèle biophysique. Étude du casd’une région montagneuse dans le nord de l’Espagne.• Les gestionnaires forestiers doivent actuellement faire face à de nombreux défis qui impliquent unbesoin croissant d’estimateurs précis de la structure et de la biomasse, de la productivité potentielleet de la croissance des forêts.• L’objectif de ce travail est la modélisation de la productivité potentielle dans une région monta-gneuse de l’Espagne. Le modèle combine des données climatiques, topographiques et lithologiqueset se base sur une variante d’un modèle biophysique classique : l’indice de Paterson.•Dans une première approche, la productivité climatique est estimée en modélisant les paramètres re-quis grâce à différentes techniques géostatistiques et de logiciels relevant des systèmes d’informationgéographique (SIG). Une deuxième approche consiste corriger les anciennes classes de productivitéen prenant en compte les facies lithologiques. Le modèle de productivité forestière potentielle a étéobtenu en combinant ces deux modèles. Finalement, les données de l’Inventaire Forestier National(IFN) sont utilisées pour comparer les rendements réels et potentiels dans les différentes régions dela zone étudiée.• Les résultats de ces analyses ont montré l’utilité du modèle, en particulier dans les régions mon-tagneuses, où aucune différence significative n’a été décelée entre les données IFN et le modèle.Ces résultats ont cependant mis aussi en évidence des divergences entre la productivité potentielle etdonnées réelles lorsque l’on compare différentes espèces, classes de diamètre ou modes de gestion.

* Corresponding author: raquel_benavides@yahoo.com

1. INTRODUCTION

Today’s forest managers face a number of important chal-lenges. One of the most critical is the need to provide forest

Article published by EDP Sciences

Ann. For. Sci. 66 (2009) 108 R. Benavides et al.

products for an increasing world population despite a shrink-ing natural-resource base challenged by climate change, de-sertification, environmental pollution, loss of biodiversity andother stresses. Forests have acquired a renewal and specialsignificance due to their key role in environment conser-vation, recreation and sustainable production as one of thebases of rural development. In current forest science research,the requirement to encompass this new paradigm involvesan increasing need for precise estimates of forest structureand biomass, potential productivity or forest growth (Tickleet al., 2001), and modelling on different scales, from stand tolandscape level. In this regard, a deep knowledge of forest pro-ductivity of the states is essential to develop forestry and landuse plans and policies (Lansberg, 2003).

Different criteria and methods have been used to evaluateforest site productivity (Vanclay, 1994). A traditional classi-fication divides the variety of approaches into phytocentric,considering the phytomass production as the ultimate measureof a site’s productivity, or geocentric methods, asserting thedependence of site productivity upon soil and climatic vari-ables. Among phytocentric approaches, the use of a site indexis broadly accepted as a surrogate for the potential productiv-ity for pure even-aged stands (Wang et al., 2005). However,there are some cases in which the site index seems to be aninappropriate tool since it is linked to a specific species andforest structure (Bravo and Montero, 2003; Bravo-Oviedo andMontero, 2005; Monserud and Sterba,1996). Hence, it is im-possible to obtain this index where there are no trees, wherethe species concerned is not present (Ung et al., 2001) or withsome specific species, e.g. Quercus spp. (Adame et al., 2006),due to their traditional management techniques (coppice orpruning) or their slow growth rate. Furthermore, a site indexshould not be used for young stands, since a slight error in es-timation at this age could lead to a much larger error, as thecurves tend to join at age zero (Goelz and Burk, 1992). Thus,alternative methods to phytocentric ones for site productivityassessment are important.

The prediction of the site index from site attributes (geocen-tric) has been researched thoroughly, although it is difficult totest them against the true site productivity (Daniel et al., 1979).Main approaches have developed models based on climatic,topographic, soil and biotic factors (Vanclay, 1994). The bestknown climatic index of forest growth is Paterson’s CVP index(Paterson, 1956) which was designed to predict the maximumgrowth potential in terms of volume production (Hägglund,1981; Johnston et al., 1967). Traditionally, this index has beenused for large areas, even on a global scale (Lemieux, 1961;Sánchez Palomares and Sánchez Serrano, 2000). Nevertheless,with the aid of new technologies and the existence of more andbetter data sets, this index can be applied on regional scales.In spite of its limitations, it can be very useful for comparingzones located within the same region, regardless of the pres-ence or absence of trees, the age of the stand or the species(Vanclay, 1994).

Simulation modelling has been proven as a practical andeffective approach for forest dynamics and yield researchthroughout time and space. In fact, it is an economicallyefficient way – maybe the only one – to investigate the

implications of different management strategies (Bravo andDíaz-Balteiro, 2004; Rodríguez Soalleiro et al., 2004), or theupscaling of productivity estimates from individual sites tolarger areas (Bernier et al., 1999; García López and AlluéCamacho, 2006; Landsberg and Waring, 1997). Besides, someother “Digital Forestry” techniques such as geographic infor-mation systems (GIS) have become some of the most usefuland widespread tools in forestry and information management(Shao and Reynolds, 2006).

The aim of this study is to review a model of potential pro-ductivity initially developed by Serrada (1976), and later re-vised by Sánchez Palomares and Sánchez Serrano (2000) formainland Spain. This model is based on a modified bioclimaticindex: the Paterson Index, weighted according to lithology. Ithas been widely used by forest managers in Spain with accept-able results on regional scales. In this study we propose newapproaches for the required inputs, using GIS and other sta-tistical tools such as geostatistical techniques to improve baseclimatic models. In addition, the results of this geocentric ap-proach are tested for the first time using actual yield data, ap-plying this methodology to a complex and mountainous regionin the North of Spain, Asturias.

2. MATERIALS AND METHODS

2.1. The study area

The study area comprises the region of Asturias in North Spain,covering an area of 10 604 km2. Its northern boundary is theCantabrian Sea (with a coastline of 354 km), and the CantabrianMountains form a natural border to the South (Fig. 1a). This regionis characterised by steep topography, with altitudes ranging from sealevel to 2 648 m in just 40 km. Thus, 80% of the territory has slopesgreater than 20% and 34.5% exceeds 50%.

2.2. Data

The initial data were the mean monthly temperatures and rain-fall obtained from the meteorological stations of the National Mete-orology Institute located in Asturias and nearby provinces (Fig. 1b).According to the World Meteorological Organisation, a 30-year pe-riod is required to establish the climatic baseline. Therefore, the1970–2000 data set was used for the modelling, previously complet-ing the missing data through regression analyses. A Digital ElevationModel (DEM) was taken as ancillary data, with a spatial resolutionof 50 m.

Data obtained from the plots of III National Forest Inventory ofSpain (NFI) (Ministry of Environment of Spain, 2003) were com-pared with the model. The forestry database in Asturias comprises atotal number of 1 877 plots, which means one plot every 240 ha. Forthis study a total of 836 plots was selected, being those which weremost significant in terms of forestry and productive species (Fig. 1).These species were Pinus sylvestris L., Pinus radiata D. Don, Pi-nus pinaster Aiton., Eucalyptus globulus Labill., Betula spp., Fagussylvatica L., Castanea sativa Mill., Quercus robur L. and Quercuspetraea (Mattuschka) Liebl., and a minimum basal area of 15% ofany of these species was required for the selection. Production data

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a)

b)

Figure 1. (a) Location of the study area, with its regions and the locations of the selected plots from the III National Forest Inventory (thenumber of plots per region -R- is: 191 for R1; 163 for R2, 59 for R3; 42 for 4Ra; 125 for R4b; 45 for R5; 50 for R6; 43 for R7; and 118 forR8). (b) Location of the selected meteorological stations to model the climatic variables (white squares are the stations with temperature data,and black circles are stations used to model rainfall data).

(annual increment in volume of wood per ha, henceforth AIVW, de-fined as m3 ha−1 yr−1) and the UTM coordinates of every plot wereobtained using the BASIFOR software (Del Río et al., 2002), version2.0. (Bravo et al., 2005) developed by the University of Valladolid(Spain). Productive data for the different tree species and diameterclasses (sorted every 10 cm) were recorded in each plot. The BASI-FOR 2.0. software uses data from the II and III NFI, comparing thevolume of every marked tree to assess the increment in volume, ac-cording to tree volume tables, and applying some factors to extendthe results per hectare.

2.3. Climatic Productivity

The Paterson Index (PI) used in this work is a variant developedby Serrada (1976).

PI =V. P.G. f

A. 12(1)

where V is the mean monthly temperature of the warmest month (◦C);A is the difference between the mean maximum temperature of thewarmest month and the mean minimum temperature of the coolest

month (both in ◦C); P is the mean annual rainfall (in mm), calculatedas the sum of the 12 mean monthly rainfall; G is the length (numberof months) of the growing period according to the Gaussen criteria(Gaussen, 1954); that is, the total number of months in which rainfall(mm) was more than double the mean temperature (in ◦C), as long asthis temperature was equal to or exceeded a minimum threshold of6 ◦C. Finally, f is the insolation factor proposed by Gandullo (1994):

f =2500

(n + 1000)(2)

where n is the number of sun hours in one year.To assess and lay out the spatial modelling of these ecological

variables, all the techniques used and exposed below were imple-mented using the software ArcGis 9.0 (ESRI, Inc., Reedlands, 2004).

The insolation factor f decreases when the number of sun hours in-creases. It is considered that the growth of forest covers in the IberianPeninsula, with frequent summer droughts and with a high number ofannual sun hours, is favoured by low insolation, which reduces evap-otranspiration and increases height growth. The number of sun hourswas estimated through an approach based on the model developedby Kumar et al. (1997). The original model consisted of a program

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Table I. Description of the productive classes and sub-classes, with their lithologic correction coefficient (C) and productivity ranges(m3 ha−1 y−1) (Serrada, 1976).

Class C Subclass Production DescriptionIa > 9.0

I 1.66 Ib 8.25–9.0 No limitation for productive forest growthIc 7.5–8.25IIa 6.75–7.50

II 1.44 IIb 6.0–6.75 Slight limitations for productive forest growthIIIa 5.25–6.0

III 1.22 IIIb 4.50–5.25 Moderate limitations for productive forest growthIVa 3.75–4.5

IV 1 IVb 3.0–3.75 Moderately severe limitations for productive forest growthVa 2.25–3.0

V 0.77 Vb 1.5–2.25 Severe limitations for productive forest growthVIa 1.0–1.5

VI 0.55 VIb 0.5–1.0 Very severe limitations for productive forest growthVII 0.33 VII < 0.5 Enough limitations to hinder the growth of any productive forestVIII 0 VIII 0 Unproductive lands

that was capable of estimating the ground radiation, even in moun-tainous regions, because it took into account both slope and aspect,and was supported by formulas which incorporated latitude, the dayof the year, the time of the day and the azimuth. In any case, thismodel only considered radiance in cloudless conditions. In the vari-ant used in this study, the hours per day when radiation measurementsexceeded 120 W m−2 (minimum threshold detected by heliographs)were computed. Estimates were assessed every 20 min.

To obtain the parameters V , A, P and G, it was necessary to modelthe monthly rainfall and mean temperatures, and the mean maximumand minimum temperatures of the warmest and the coolest months,respectively. First, data from meteorological stations for a 30-year pe-riod were selected (1970–2000), refined, filtered and completed withregression analysis, and then the modelling was carried out using geo-statistical techniques, attempting to identify the approach which gavethe least estimation errors. Full details of the techniques applied canbe found in Benavides et al. (2007), in which 5 geostatistical methodswere compared for estimating the mean January and August temper-atures in Asturias. In the present study, the five geostatistical tech-niques were compared for the monthly rainfall and temperature esti-mates. The methods included ordinary kriging (OK), developed in theXY plane and in the X, Y and Z axes (OKxyz), with zonal anisotropyin the Z axis, along with three techniques that included elevation fromthe DEM as an explanatory variable: ordinary kriging with externaldrift (OKED) and universal kriging, using the Ordinary Least Squaresresiduals to estimate the variogram (UK1) or the Generalised LeastSquares residuals (UK2). The spatial resolution of the resulting mod-els was a pixel size of 0.25 km2. Once the models were mapped, themean error or bias (ME) and the mean absolute error (MAE) at theobserved points were computed to determine the accuracy of the dif-ferent approaches.

2.4. Potential versus real forest productivity

Apart from climate, soil is another important factor related to plantgrowth and as such, should be taken into account (Bravo-Oviedoand Montero, 2005; Milner et al., 1996; Wang et al., 2005). Hence,a correction of the climatic productivity was carried out based onthe lithology map of Asturias on a 1:25 000 scale (Environmental

and Territorial Cartography Centre of Asturias), previously rasterisedwith a spatial resolution of 10 m. The different types of facies weresorted into eight productive classes, according to the productive char-acteristics of the soils normally derived from them. Next, each pro-ductive class was given a correction coefficient (C) according to thevalues given in Table I (Sánchez Palomares and Sánchez Serrano,2000). These coefficients resulted from a study of the yield tables ofnative species under similar management regimes, inferring that yieldvariations were attributable to differences in soils.

The relationship between the PI and the real productivity was as-sessed through Equation (3), an algorithm developed by Paterson andvalidated for mainland Spain by Serrada (1976). Hence, the map ofpotential forest productivity (PP) for Asturias was obtained throughEquation (4), with the previously modelled input variables. The cli-matic variable models were resized to reach the same pixel size asthe lithological input; thus, the spatial resolution of the output waslikewise 10 m. Then the land was classified into different productiveclasses (Tab. I) according to the resulting figures.

PP = 5.3 · log PI − 7.4 (3)

PP = C · 5.3 · log

(V f PG

A12

)− 7.4. (4)

Once the potential productivity model was mapped, their values inevery plot previously selected from the NFI were compared with thereal figures. In the present study, Asturias was divided into 8 regions(Fig. 1). Each region is similar in terms of the environment, popula-tion, main economic sectors, and the quality and quantity of infras-tructure, equipment and communications. Region 4 was subdividedsince the area was very large and had two very distinct regions: amountainous part (4a) and an inner part (4b).

Correlations and univariate analyses of variances were carriedout in each of the 9 regions, using the SPSS software (SPSS, Inc.,Chicago, 2004). The analysis of variance made it possible to iden-tify in every region where the real data (AIVW) from the NFI, withall the main species pooled together, and the potential productivitydata (obtained from the model) were similar, and where they werenot. Then, correlation analyses were carried out to identify the fac-tors which contributed to the dissimilarities between the two data sets;

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Table II. Mean Error (ME) and Mean Absolute Error (MAE) obtained estimating mean monthly temperatures (T) and rainfall (R), and the meanminimum temperature of January (MinJ) and mean maximum temperature of August (MaxAg), with different techniques: Ordinary Kriging(OK) in the XY plane, and with anisotropy in the Z axis (OKxyz), Ordinary Kriging with External Drift (OKED) and two variants of UniversalKriging (UK1 and UK2).

January February March April May June July August September October November December MinJ MaxAg

T (◦C) ME OK 0.05 0.03 0.05 0.04 0.04 0.02 0.06 0.03 0.03 0.04 0.05 0.05 0.10 0.03

OKxyz 0.02 0.02 0.00 0.03 0.02 0.01 0.05 0.01 0.04 0.03 0.04 0.03 0.02 –0.01

OKED 0.02 0.01 0.02 0.02 0.02 0.03 0.04 0.03 0.03 0.03 0.02 0.04 0.02 –

UK1 0.02 0.01 0.02 0.02 0.02 0.03 0.04 0.03 0.04 0.03 0.02 0.03 0.02 –

UK2 0.02 0.01 0.03 0.03 0.02 0.09 0.05 0.03 0.03 0.03 0.03 0.03 0.03 –

MAE OK 0.73 0.74 0.76 0.83 0.82 0.80 0.80 0.79 0.76 0.71 0.69 0.69 0.87 1.05

OKxyz 0.67 0.57 0.55 0.52 0.49 0.51 0.49 0.57 0.51 0.54 0.57 0.77 0.67 0.80

OKED 0.77 0.62 0.55 0.53 0.55 0.61 0.67 0.62 0.48 0.51 0.65 0.58 1.09 –

UK1 0.79 0.60 0.55 0.54 0.53 0.61 0.65 0.62 0.51 0.52 0.65 0.79 1.09 –

UK2 0.78 0.62 0.56 0.57 0.53 0.63 0.57 0.61 0.53 0.57 0.66 0.61 1.00 –

R (mm) ME OK 0.13 0.10 0.17 0.19 0.08 0.09 0.25 0.18 0.06 0.37 –0.07 –0.18 – –

OKxyz –0.42 –0.28 –0.22 –0.13 –0.11 –0.06 0.13 0.21 –0.05 0.15 –0.10 –0.33 – –

OKED –0.04 –0.12 –0.02 0.06 –0.05 –0.01 0.17 – –0.06 0.17 –0.20 0.16 – –

UK1 –0.06 –0.14 –0.02 0.12 0.06 –0.02 0.16 – –0.08 0.15 –0.25 –0.33 – –

UK2 0.02 0.04 –0.06 –0.03 –0.08 –0.02 –0.02 – 0.06 0.19 –0.24 –0.32 – –

MAE OK 13.42 13.44 13.73 14.59 11.89 7.33 6.84 7.73 9.03 11.85 15.32 18.29 – –

OKxyz 13.31 12.92 13.96 16.44 11.03 7.02 6.83 8.36 8.83 11.66 15.76 17.21 – –

OKED 12.76 12.62 13.48 14.12 10.65 6.76 6.56 – 9.21 10.59 14.67 17.81 – –

UK1 12.82 12.76 13.48 14.68 11.97 6.80 6.60 – 8.66 10.67 14.81 17.21 – –

UK2 12.80 12.71 13.12 13.89 10.47 6.67 6.22 – 8.59 10.67 14.81 16.89 – –

thus, the AIVW data were correlated with variables resulting from themanagement such as the type of tree species (slow- and fast-growingspecies), the diameter classes and the stems per ha.

3. RESULTS

3.1. Modelling the ecological variables

The monthly rainfall, mean temperatures, and mean maxi-mum and minimum temperatures of the extreme months werespatially modelled using the five geostatistical techniques,generating regional maps from point data (Fig. 1b) previouslyanalysed (filtered, and completed by estimating missing datawith regression analysis) for each month. The errors associ-ated with the different methods can be seen in Table II. Theestimates were more precise when elevation data were takeninto account. Hence, OKxyz was proven to be the best andselected to model the temperatures and UK2 for rainfall mod-elling. The mean rainfall of August was an exception becauseno correlation was found between the variable and the eleva-tion, therefore OK was run with the lowest error.

It should be noted that temperature errors were inferiorto ± 1◦C and were fairly unbiased since the mean errors werevery close to zero. In general, the errors in summer predic-tions were smaller than those for winter. With regard to rain-fall, the absolute residuals were lower in summer, coincidingwith the drier season. However, errors in spring and autumn

were proportionally inferior as the rainfall was more regularduring these months. On average, the value of MAE was 10%of the predicted rainfall.

Once the kriging techniques had been selected and themonthly climate models developed, the parameters A, V ,P and G (required for the Paterson Index) were mapped(Figs. 2a–2d). Fig. 2e shows the insolation factor (Gandullo,1994) assessed after calculating the number of annual sunhours. It can be noticed that the flat regions and South-facinghillsides presented the lowest f value since they received thehighest number of sun hours. Finally, by implementing Equa-tion (1), we obtained the potential climatic productivity map(Fig. 3a).

3.2. Potential Forest Productivity

The correction factor derived from the lithology wasmapped (Fig. 3b) according to Table I. The final step was torepresent the potential productivity estimates (Fig. 4a) gener-ated by using Equation (4) with the modelled inputs. The pro-ductivity figures ranged from 2.91 to 13.11 m3 ha−1 y−1.

3.3. Data from the III National Forest Inventory

The Analysis of Variance showed that the production data(m3 ha−1 y−1) did not differ significantly (p < 0.05) when com-paring the actual values with those of our model for regions 2,

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Figure 2. Modelled inputs to assess the Paterson Index: (a) number of vegetation active months; (b) mean temperature of August, in ◦C; (c)annual rainfall, in mm; (d) thermic fluctuation, in ◦C; (e) insolation coefficient.

Figure 3. (a) Map of the Paterson Index model obtained in Asturias using the previously modelled inputs (Fig. 2); (b) map of the correctioncoefficients due to lithology, obtained after classifying the types of facies and using Serrada’s correction factor (Serrada, 1976).

4a, 6 and 8 (Tab. III). These four regions comprised all themountainous regions with high altitudes and steep slopes. Re-gion 7 was the only mountainous region missing from this list.

A detailed study of the remaining regions showed that thedifferences between paired data (real versus potential pro-ductivity) may be the result of management factors. It wasfound that the type of species, the age and the stocking ratewere factors which significantly influenced the real production(Tab. IV). The main factor affecting the AIVW was the tree

density, with a positive correlation coefficient of ρ = 0.800∗∗when data for the whole of Asturias were pooled together. Thetype of tree species (fast-versus slow-growing) and the diame-ter classes also showed significant correlation with IAVW, butnegative (ρ = −0.609∗∗ and ρ = −0.530∗∗, respectively).

It was found that regions 1, 3 and 4.b (less mountainousand closer to the coast) have a real productivity higher thanthe potential one, with negative values resulting from the sub-traction between real and potential averages (Tab. V). Higher

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Figure 4. (a) Potential forest productivity map modelled using the new techniques (geostatistics, GIS), (b) potential forest productivity modelassessed by Sánchez-Palomares and Sánchez Serrano (2000).

Table III. Effect of the origin of data (National Forestry Inventoryversus Model) on the productivity (m3 ha−1 y−1), in the different re-gions of Asturias.

Region N Mean S.E.M. Sig. (p-value)

NFI Model

1 191 11.066 7.108 0.733 0.000

2 163 6.647 5.546 0.627 0.215

3 59 17.366 8.103 1.325 0.000

4a 42 5.856 6.452 0.646 0.516

4b 125 11.714 7.373 0.914 0.001

5 45 14.260 7.997 1.544 0.005

6 50 6.215 7.888 0.588 0.051

7 43 3.912 7.967 0.485 0.000

8 118 9.213 7.739 0.753 0.168

S.E.M.: standard error of the mean; N: number of data pair.

AIVW was correlated with the existence of high-yielding trees(mainly eucalyptus), with high stocking rates and low diame-ter classes.

As regards region 7, the real values also differed signifi-cantly from the potential values (Tab. III), although in this casethe former were lower (Tab. V). This appears to be due to thecomplex orography of the region and the influence this has onthe species found in the plots (only slow-growing species).

Table IV. Correlation coefficients between the data of AIVWand main management factors: type of species (S ) – fast orlow-growing –, number of trees per plot (N) and diameter classes(DC).

Region S N DC

1 (n = 942) –0.516** 0.740** –0.263**

2 (n = 1028) –0.500** 0.833** –0.570**

3 (n = 448) –0.531** 0.768** –0.415**

4a (n = 394) –0.178** 0.871** –0.644**

4b (n = 854) –0.550** 0.800** –0.514**

AIVW 5 (n = 361) –0.579** 0.739** –0.352**

(m3ha−1y−1) 6 (n = 276) –0.234** 0.860** –0.590**

7 (n = 231) – 0.881** –0.685**

8 (n = 905) –0.538** 0.830** –0.601**

total area–0.609** 0.800** –0.530**

(n = 5439)

When real yield figures are considered separately for dif-ferent species and at different ages, the analysis of varianceshowed no similarities with the values of the model. That isbecause we cannot extract from the model information for dif-ferent age classes or tree species as it shows potential produc-tivity yields.

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Table V. Descriptive statistics of the variables SUBTRACTION (be-tween the potential productivity, PP, and the AIVW) and the RATIO(division between the AIVW and PP).

RegionSubtraction Ratio

Mean SD Mean SD

1 –1.63 7.08 1.43 1.222 0.89 4.54 0.88 0.913 –4.37 8.79 1.69 1.294a 1.72 5.81 0.78 0.714b 0.54 6.77 0.98 0.935 –2.24 7.88 1.32 1.036 1.87 5.95 0.78 0.767 3.88 3.18 0.53 0.418 1.87 5.65 0.82 0.81

SD: Standard deviation.

4. DISCUSSION

4.1. Productivity modelling

Most climatic models previously developed have used apixel size of at least 1 km2 (Goodale et al. 1998; Hudson andWackernagel, 1994). However, as elevation and temperaturecan vary dramatically in mountainous regions, a smaller grid,0.25 km2 pixel size, was chosen in this study.

The errors made with the geostatistics techniques were ac-ceptable, especially considering the complex topography. It isremarkable that errors made in summer temperature predic-tions were smaller than those made in winter. This is due tothe higher variability in the cold season data and agrees with asimilar trend found by Rolland (2002) in Alpine regions, andby Benavides et al. (2007) in Asturias. A visual appreciation ofthe variables related to air temperature figures (Fig. 2) revealsthe well-known correlation between the temperature estimatesand the altitude (Stoutjesdijk and Barkman, 1992). The esti-mates became progressively cooler when moving inland fromthe coast towards the mountains in the South, and the growingseason was found to be longer and the thermic ranges smallerin coastal areas than in the Cantabrian Mountain range. How-ever, the warmest regions in summer corresponded to the innerbasin of the main rivers due to the “buffering effect” of the sea(Benavides et al., 2007).

The fact that rainfall is greatest in mountainous areas sug-gests that elevation again plays an important role. Other au-thors have already detected and quantified this phenomenon(Goovaerts, 2000; Havesi et al., 1992). It can also be observedthat the western part of the area registered higher values thanthe eastern part. This is due to the predominance of weatherfronts from the NW (Marquínez et al., 2003).

Bearing all this in mind, the figures for the climatic pro-ductivity index ranged from 245 to 1417, exceeding the valueof 25 which is considered the threshold value for natural re-generation of a forest (Gandullo, 1994). The model developedindicated higher potential productivity in low, flat areas, closerto the sea, because these registered warmer temperatures, a

smaller thermic range and a longer growing season. Therewere also some differences between the East and West whichmay be due to the weather fronts predominantly entering.

The influence of lithology on the productivity map can beclearly seen. The climatic productivity appeared as a continu-ous variable, similar to the behaviour of the climatic and topo-graphic variables (adjacent points registered similar values forthe variables). However, the lithology presented abrupt transi-tions on our scale. A strip of land can be identified in the west-ern half of the region, crossing Asturias from North to South,where correction factor values were low. This was due to thecharacteristics of the lithology: quartzites that give rise to acidsoils with many outcrop rocks.

Comparing these results with those of the previous modelrepresented in Figure 4b. and developed by Sánchez Palo-mares and Sánchez Serrano (2000), a more detailed perfor-mance of the newer model can be appreciated. On one hand,a more accurate scale of the lithology map was used (from1:50 000 to 1:25 000). On the other hand, the use of geosta-tistical interpolations and the advantages offered by the GISallow us to obtain more precise information on the ecologi-cal variables throughout the region, especially in mountainousregions where modelling is always difficult and challenging(Carrega, 1995). Hence, an altitudinal gradient can be distin-guished in the present model, but not in the earlier study. In theold model, 77.4% of the Asturian surface was considered a re-gion with maximum climatic productivity (Ia > 9 m3 ha−1 y−1)compared with 27.3% in our case, and the lithology was theonly clearly stated factor that resulted in lower productivity.However, this picture does not appear to reflect the real situ-ation as it does not take into account the fall in temperatureassociated with altitude, an important variable affecting vege-tation growth (Landsberg and Waring, 1997; Ni, 2004).

4.2. Usefulness for land use planning

This approach has been widely used for decades and itspractical implementation has proved its worth for silvicul-tural planning in Spain, together with other more specificstudies, focused on assessing the site potentiality for certaintree species (Bravo-Oviedo and Montero, 2005; García Lópezand Allué Camacho, 2006). Its incorporation into the for-est managers’ decision-making process is an important mile-stone which many productivity models do not attain (Battagliaand Sands, 1998). In spite of the usefulness of the model,its validation can be somewhat complex due to the lack ofadequate data for directly testing the potential productivityestimates. It is difficult to separate the site, stocking, age,structure and species effects when analysing plot growth data,especially with mixed or uneven-aged stands (Milner et al.,1996). In a mountainous region the ecological variables mayalso differ significantly from the estimates because the sam-ples are usually scarcer. The climatic variables in Asturiaswere tested with an acceptable level of errors by Benavideset al. (2007), particularly bearing in mind that the greatest er-rors were detected at the highest altitudes, above the altitu-dinal limit of the forest. The lithology was simply proposed

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Modelling of potential productivity Ann. For. Sci. 66 (2009) 108

as an approximate description of soil characteristics, but thelack of correlation between the real productivity and the litho-logical coefficient (data not shown) suggests that other factorscontribute greatly to the development of the soil, especiallyin mountainous regions. These factors include slope, altitude(Odeh et al., 1994), rainfall, and historic and current land man-agement practices, e.g. the existence or absence of vegeta-tion cover, soil preparation or fertilisation particularly for fast-growing species plantations, or the use of fire as a managementtool (Fernández et al., 2005).

A significant correlation between the two databases (realand potential) can be observed, thus partially validating ourmodel. However, the value of the coefficient is small (ρ =0.203∗∗), highlighting the aforementioned difficulties involvedin assessing potential productivity and the differences betweenthe two data sets. The statistical analysis showed that ourmodel was capable of generating values similar to the realvalues in mountainous regions, when all the species and agesare pooled. This is especially relevant given the difficulty inmodelling areas with complex topography. Conversely, in flatareas close to the sea, the real figures exceeded the potentialones due to the management practices and the existence of eu-calyptus (Eucalyptus globulus Labill.) stands, which is exotichigh-yielding forest species, managed at high densities usingshort rotations.

Moreover, the evaluation of the coefficients of the poten-tial productivity formula (Eqs. (3) and (4)) may be biasedwhen it is used in small areas, because Paterson (1956) in-cluded in the statistical analysis data from large areas with agreat diversity of annual growth rates, and Serrada (1976) val-idated Paterson’s approach using data from plots located allover the Iberian Peninsula, including the Mediterranean area,which in general terms has lower productivity rates than As-turias (less favourable climatic conditions) but covers a largersurface area. In addition, the advances made in terms of genet-ics (new clones with better yield rates) and the new technicalknowledge (silvicultural performances) might also affect theresults, which were not contemplated when the original modelwas developed.

To sum up, it should be stated that this model has a numberof limitations which should be borne in mind. The spatial inter-polations are smoothing techniques, and therefore, introduceerrors which can be propagated to the model output. More-over, the accuracy of the prediction may improve when usingan accurate model for soil. However, where precise edaphicinformation is not available, it would be more costly to obtainthis data in situ rather than using the lithology map.

Further research is required in order to refine and improvethe assessment of potential productivity and its implementa-tion as a management tool. In the meantime, the present modelcan be used, bearing in mind its limitations, to define the areason a regional scale where productivity is potentially the high-est, regardless of the existing management practices (density,ages, silvicultural actions) or tree species. It also allows us toevaluate the current state of the forest stands, defining areas,species and management methods which produce yields aboveor below the potential productivity figures. This possibility is

very useful both for land use planning and for aiding forestmanagers to make appropriate decisions.

Acknowledgements: We wish to thank Miguel Ángel Álvarez, Di-rector of the Instituto de Recursos Naturales y Ordenación del Terri-torio (INDUROT). We are also grateful to Dr. Otilio Sánchez from theINIA (Spanish Institute of Agrarian Research) for reviewing the clas-sification of the lithology map, and to Dr. Fernando Montes and Dr.Agustín Rubio from the Polytechnic University of Madrid, for collab-orating with geostatistical techniques. The research was supported bya fellowship awarded to R. Benavides from the Ministry of Educationand Science of Spain, in the context of project AGL2003-05342.

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